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WASHINGTON — Presidents at 42 private colleges scaled the $1 million annual mark in total pay and benefits in 2011 — a slight bump from the year before, according to a survey based on the latest federal tax information from the 500 private schools with the largest endowments.

Total median compensation was $410,523, or 3.2 percent more.

A high salary can be a sign of prestige for presidents, but it also opens them to criticism. The Obama administration and consumers are pressuring schools to rein in tuition costs, increase graduation rates and strengthen the value of a diploma.

The Chronicle of Higher Education’s report released Sunday used federal tax information from 2011, the most recent available.

The top earner in the survey was Robert J. Zimmer, the president of the University of Chicago. His base pay was $918,000, but his total compensation was $3.4 million. About 40 percent of his total earnings stem from deferred compensation — a retention tool commonly used to keep college presidents on the job longer, according to the Chronicle.

Typically, presidents lose the deferred compensation if they leave early, and many of the top earners in the survey received deferred compensation in 2011.

The analysis included a comparison of presidents’ salaries compared with the size of their college’s budget. By that measure, the median pay was $5,466 per $1 million of expenses.

Zimmer, it found, earned $1,113 for every $1 million in expenses at his college because the budget was $3 billion.

By comparison, Drew Gilpin Faust, the president of Harvard University, didn’t do as well as some of her peers. She earned $230 for every $1 million in expenses. Her total compensation was $899,734, while the university’s budget was $3.9 billion, according to the Chronicle.

On the other end, several presidents who are members of religious orders earned no compensation at Roman Catholic institutions, the report said.

In 2010, 36 presidents earned more than $1 million in compensation.

The median base salary was $301,299 in 2011, slightly more than the year before.

A previously published report by the Chronicle examined the salaries of public college presidents from the 2011-2012 budget year. It found that four earned more than $1 million in compensation. The median total compensation was $441,392, or 4.7 percent more than from the previous year.